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On the L2 continuity of a class of pseudo differential operators

On the L2 continuity of a class of pseudo differential operators

with X, ~o, ~ fixed weight functions on ~+ = {~ER, 4=>0}. Our aim is to give necessary and sufficient conditions for the weight functions i n order that the operators (0-1) are continuous on LZ(R). As a matter of fact, we shall restrict ourselves to the one-dimensional case, n …